Symmetry Breaking Induced Geometric Surfaces with Topological Curves in Quantum and Classical Dynamics of the SU(2) Coupled Oscillators

In the three‐dimensional (3D) transversely symmetric oscillator, there are plentiful degeneracies and gaps in the quantum energy spectrum as a function of the ratio of the transverse to longitudinal frequency. It is theoretically verified that while the SU(2) interaction destroys the original degeneracies, numerous new degeneracies and gaps emerge around the original degeneracies to form a similar fine energy spectrum. The classical trajectories at the emergent degeneracies are analyzed to be localized on the 3D parametric surfaces which are constituted by the topologically invariant curves in the transverse tomography. The quantum coherent states are exploited to develop the wave functions that correspond to the 3D geometric surfaces in classical dynamics. Furthermore, the wave structures of the stationary coherent states at small quantum numbers are explored and found to display peculiar patterns with symmetries related to classical trajectories.     

Interfering with the neutron spin

Charge neutrality, a spin 1/2 and an associated magnetic moment of the neutron make it an ideal probe of quantal spinor evolutions. Polarized neutron interferometry in magnetic field Hamiltonians has thus scored several firsts such as direct verification of Pauli anticommutation, experimental separation of geometric and dynamical phases and observation of non-cyclic amplitudes and phases. This paper provides a flavour of the physics learnt from such experiments.     

格点定模SU（2）－Higgs模型的解析计算

对格点上基础表示的定模Ｈｉｇｇｓ场与ＳＵ（２）规范场耦合系统的相图进行解析计算至累积展开的第四级，用扫瞄确定变分参数的方法，得到与ＭｏｎｔｅＣａｒｌｏ模拟很好符合的相图．计算了Ｎ＿τ＝１的有限温度情形下ＳＵ（２）－Ｈｉｇｇｓ系统和纯ＳＵ（２）模型的Ｐｏｌｙａｋｏｖ线＜Ｌ＞，对后者得到迄今最佳的近似解析结果βｃ。     

Exact Solutions for Self-Dual SU(2) and SU(3) Yang–Mills Fields

The (constrained) canonical reduction of four-dimensional self-dual SU(2) and SU(3) Yang–Mills theory to two-dimensional nonlinear Schrödinger (NS) and Korteweg–de Vries (KdV) equations are considered. The Bäcklund transformations (BTs) are implemented to obtain new classes of exact solutions for the reduced two-dimensional NS and KdV models.     

格点变模SU（2）－Higgs模型的解析计算

在四维空间对格点ＳＵ（２）－Ｈｉｇｇｓ模型的序参量Ｅｐ＝〈ｔｒＵｐ〉〉用累积展开计算到四级近似．Ｈｉｇｇｓ场为基础表示．发展了定双变分参数的办法．得到的相图与蒙特卡罗结果有好的符合．     

SU（2）相干态场与二能级原子的非简并双光子相互作用

研究了双模ＳＵ（２）相干态场与腔中二能级原子的非简并双光子相互作用。用数值计算讨论了ＳＵ（２）光场的反关联特性对原子动力学行的影响及场的量子统计性质时间的演化。     

SU (2) lattice gauge theory simulations on Fermi GPUs

In this work we explore the performance of CUDA in quenched lattice SU (2) simulations. CUDA, NVIDIA Compute Unified Device Architecture, is a hardware and software architecture developed by NVIDIA for computing on the GPU. We present an analysis and performance comparison between the GPU and CPU in single and double precision. Analyses with multiple GPUs and two different architectures (G200 and Fermi architectures) are also presented. In order to obtain a high performance, the code must be optimized for the GPU architecture, i.e., an implementation that exploits the memory hierarchy of the CUDA programming model.     

Tree-level breaking of SU(2)×U(1) in general SUGRA theories

It is shown that SU(2)×U(1) can be broken at the tree level, without the occurrence of global potential minima that break U(1)_e.m., in supergravity models that are more general than those proposed by Nilles, Srednicki and Wyler. The study comprises an analysis of models with a general soft supersymmetry-breaking structure as well as those of the Hall-Lykken-Weinberg type.     

Vector and Spinor Decomposition of SU（2） Gauge Potential, Their Equivalence, and Knot Structure in SU（2） Chern-Simons Theory

In this paper, spinor and vector decompositions of SU（2） gauge potential are presented and their equivalence is constructed using a simply proposal. We also obtain the action of Faddeev nonlinear 0（3） sigma model from the SU（2） mass/ve gauge field theory, which is proposed according to the gauge invariant principle. At last, the knot structure in SU（2） Chern-Simons filed theory is discussed in terms of the Φ-mapping topological current theory, The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of Φ-mapping.     

利用SU（2）_（q，s）量子代数的两参数变形振子实现讨论SU（2）_（q，s）相干态

利用ＳＵ（２）ｑ，ｓ量子代数的两参数变形振子实现构造出与Ｐｅｒｅｌｏｍｏｖ相干态形式不同的ＳＵ（２）ｑ，ｓ相干态．证明了ＳＵ（２）ｑ，ｓ，量子代数的表示基是正交的，并讨论了它的相干态的归一性和完备性．指出ＳＵ（２）ｑ，ｓ相干态的相干性受参数ｑ，ｓ的影响，它比单参数变形ＳＵ（２）ｑ相干态更具一般性．     

利用原子-腔场的拉曼相互作用制备双模SU(2)薛定谔猫态

利用一个参量频率转换过程,在腔中制备双模ＳＵ（２）相干态,然后注入一个与腔场的一个个模发生拉曼相互作用的Ａ型三能级原子,通过原子－腔场相互作用生成腔场－原子纠缠,通过对原子进行选择性测量,腔场－原子纠缠态将塌缩到纯态,即双模ＳＵ（２）薛定谔猫态。     

SU(2)纯格点规范场热力学非对称点阵Monte-Carlo模拟

在非对称点阵(ξ=2,3)上模拟了SU(2)纯格点规范场系统的热力学行为,结果表明,非对称点阵Monte-Carlo模拟是实现快速趋向连续物理极限的有效途径.     

Effective Lagrangian of SU（2） Yang—Mills Theory in the Presence of Fermions

We derive the one-loop effective action of SU(2) Yang-Mills theory in the presence of fermions in the low energy limit.This result is presented by separating the topological degrees,which describe the non-Abelian monopoles from the dynamical degrees of the gauge potential and integrate out all the dynamical degrees and fermions in SU(2) Yang-Mills theory.     

SU(2)Thirring模型边界算子的Boson表达式

得到了有边界的SU(2)Thirring模型的反射矩阵Rab(θ),以及相应的边界算子的Boson表达式.     

SU(2)群的非齐次逆微分实现

利用玻色振子的逆算符构造了SU(2)群的生成元和不可约表示的相干态,进而导出了SU(2)群的非齐次逆微分实现.     

EPR Entangled States for Bipartite Kinematics and New Bosonic Representation of SU(2) Algebra

We find that the Einstein-Podolsky-Rosen (EPR) entangled state representation describing bipartite kinematics is closely related to a new Bose operator realization of SU(2) Lie algebra. By virtue of the new realization some Hamiltonian eigenfunction equation can be directly converted to the generalized confluent equation in the EPR entangled state representation and its solution is obtainable. This thus provides a new approach for studying dynamics of angular momentum systems.     

EPR Entangled States for Bipartite Kinematics and New Bosonic Representation of SU（2） Algebra

We find that the Einstein-Podolsky-Rosen (EPR) entangled state representation descr/bing bipartite kinematics is closely related to a new Bose operator realization of SU(2) Lie algebra. By virtue of the new realization some ttamiltonian eigenfunction equation can be directly converted to the generalized confluent equation in the EPR entangled state representation and its solution is obtainable. This thus provides a new approach for studying dynamics of angular momentum systems.     

含时调制的Jaynes-Cummings模型的Pancharatnam相位

基于含时调制的Jaynes-Cummings模型的SU(2)群结构,求得它的Pancharatnam相位,并分析 了该模型从绝热开启直到关闭原子与场的相互作用的整个过程的相位变化.讨论了该模型在 半经典近似条件下的情况. 关键词： 含时调制的Jaynes-Cummings模型 Pancharatnam相位 SU(2)群